Part A : A machine that bottles apple juice is set so that every 6th bottle gets a red label and every 9th bottle gets a blue cap. The machine.
Part B :
The machine is reset so that every 10th bottle gets a special gold band around the label. What number bottle will be the first to get a red label, a blue cap, and a gold band ?

The 90th

Step-by-step explanation:

You have to find the least common multiple of 6, 9, and 10 because that will be the first one when all three are on the bottle.

The least common multiple is 90.

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!